Pumped storage hydro electric power plant is planned. If I decide now to go more deep and lower the center line of horizontal machine what will be the effect of the same on the turbine performance viz. Output, efficiency, size, speed, etc.
Whether pumping head will increase resulting into more energy required for pumping.

I am not understanding what you are trying to say at all.

But if your water storage is higher than initially, the turbine will get a higher velocity of water striking it.